CP physics Final review sheet-1: Vibrations and Waves
1) Does Simple Harmonic Motion occur when the force, acting on a mass, is positively proportional to the displacement (F = kx)? Explain.
Answer: No. F = kx (k positive) leads to unconstrained motion. One must have the force in opposite direction, F = -kx, to produce SHM.
Diff: 2Var: 1Page Ref: Sec. 13.1
2) What is the equation of motion of a 30. gram mass on a spring of stiffness 3.0 N/m if it is initially displaced 7.7 cm and released?
Answer: y = 7.7 cos(10 t) where y is in cm and t in seconds.
Diff: 2Var: 1Page Ref: Sec. 13.2
3) SHM may be written y = A sin( ωt + φ ).
What is the value of φ, the phase constant, when:
(a)the initial displacement is zero?
(b)the initial displacement is A?
(c)the initial velocity is zero?
Answer:
(a)φ = 0
(b)φ = π
(c)φ = +π or -π
Diff: 2Var: 1Page Ref: Sec. 13.2
4) Spock has landed on a newly discovered planet and is instructed to determine its gravitational strength. He constructs a simple pendulum with a length of 700. mm and observes 20. full swings in 1 minute and 16.7 seconds. What does he deduce the "acceleration of gravity" to be from this?
Answer: g = 1.88 m/s2
Diff: 2Var: 1Page Ref: Sec. 13.2
FIGURE 13-1
5) Shown in Fig. 13-1 is a graph of position vs. time for a system undergoing simple harmonic motion. Which of the other graphs represents the system's acceleration as a function of time?
Answer: (a)
Diff: 2Var: 1Page Ref: Sec. 13.2
6) How would you "weigh" the astronauts in orbit (where they feel weightless) so that you can keep them in good health?
Answer: You could determine their MASS by harnessing them to springs, setting them to oscillate (SHM) and timing their period of oscillation. Knowing the "spring constant" allows one to calculate the mass. [Remember ω2 = k/m]
Diff: 3Var: 1Page Ref: Sec. 13.2
7) Imagine hitting a heavy anvil with a hammer. The hammer is in contact with the metal for a short period of time. How do you suppose the time of contact depends upon how hard you hit the anvil (i.e., does a hard hit remain in contact much longer or shorter than a light tap?) [It is reasonable to assume Hooke's law of elasticity to hold.]
Answer: The anvil has an effective elastic constant which is relatively large. The time of contact does NOT depend upon the strength of the blow. The PERIOD of oscillation (the time in contact is half a period!) is independent of the amplitude for SHM.
Diff: 3Var: 1Page Ref: Sec. 13.2
8) Give at least one example of each of the following:
(a)longitudinal standing wave.
(b)transverse standing wave.
Answer:
(a)sound wave resonating in an organ pipe
(b)vibrating string on a violin
Diff: 2Var: 1Page Ref: Sec. 13.3
9) Name 5 different type of waves or wave motion.
Answer: sound, light, water waves, earthquake waves, waves on a plucked string
Diff: 2Var: 1Page Ref: Sec. 13.3
10) Why can longitudinal earthquake waves go straight through the center of the Earth but transverse waves cannot?
Answer: The transverse wave can not traverse the outer liquid core.
Diff: 2Var: 1Page Ref: Sec. 13.3
11) State the Principle of Superposition.
Answer: At any time, the combined waveforms of two or more interfering waves is given by the sum of the displacement of the individual waves at each point in the medium.
Diff: 1Var: 1Page Ref: Sec. 13.4
12) Any oscillating system for which the net restoring force is directly proportional to the displacement is said to exhibit simple harmonic motion.
Answer: TRUE
Diff: 1Var: 1Page Ref: Sec. 13.1
13) Simple harmonic motion is always sinusoidal.
Answer: TRUE
Diff: 1Var: 1Page Ref: Sec. 13.1
14) The projection of circular motion onto a straight line is simple harmonic motion.
Answer: TRUE
Diff: 1Var: 1Page Ref: Sec. 13.2
15) The period and frequency of a simple pendulum depend on the mass of the pendulum bob.
Answer: FALSE
Diff: 1Var: 1Page Ref: Sec. 13.2
16) When the speed of a wave depends on the wavelength (or frequency), the waves are said to exhibit diffraction.
Answer: FALSE
Diff: 1Var: 1Page Ref: Sec. 13.4
17) The condition of driving a system at a natural frequency is referred to as resonance.
Answer: TRUE
Diff: 1Var: 1Page Ref: Sec. 13.4
18) The total energy stored in simple harmonic motion is proportional to the
A) amplitude.
B) square of the spring constant.
C) reciprocal of the spring constant.
D) square of the amplitude.
E) frequency of motion.
Answer: D
Diff: 1Var: 1Page Ref: Sec. 13.1
19) Simple Harmonic Motion is characterized by
A) constant acceleration.
B) acceleration proportional to the acceleration of gravity.
C) acceleration proportional to displacement.
D) acceleration proportional to velocity.
E) acceleration inversely proportional to velocity.
Answer: C
Diff: 2Var: 1Page Ref: Sec. 13.1
20) Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?
A) produces no change
B) increases the energy by a factor of three
C) increases the energy by a factor of four
D) increases the energy by a factor of two
E) increases the energy by a factor of
Answer: C
Diff: 2Var: 1Page Ref: Sec. 13.1
21) A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?
A) at either A or B
B) midway between A and B
C) one-fourth of the way between A and B
Answer: B
Diff: 2Var: 1Page Ref: Sec. 13.1
22) A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a minimum?
A) midway between A or B
B) at either A or B
C) one-fourth of the way between A and B
Answer: B
Diff: 2Var: 1Page Ref: Sec. 13.1
23) Two masses, A and B, are attached to different springs. Mass A vibrates with an amplitude of 8 cm at a frequency of 10 Hz and mass B vibrates with an amplitude of 5 cm at a frequency of 16 Hz. How does the maximum speed of A compare to the maximum speed of B?
A) Mass A has the greater maximum speed.
B) Mass B has the greater maximum speed.
C) They are equal.
Answer: C
Diff: 2Var: 1Page Ref: Sec. 13.1
FIGURE 13-2
24) A mass swinging on the end of a massless string, as shown in Fig. 13-2, undergoes SHM. Where is the instantaneous acceleration of the mass greatest?
A) A and C
B) B
C) C
D) A and D
E) A and B
Answer: D
Diff: 2Var: 1Page Ref: Sec. 13.1
25) Doubling only the amplitude of a vibrating mass-on-a-spring system produces what effect on the system frequency?
A) increases the frequency by a factor of 5
B) increases the frequency by a factor of 4
C) increases the frequency by a factor of 3
D) increases the frequency by a factor of 2
E) produces no change
Answer: E
Diff: 1Var: 1Page Ref: Sec. 13.2
26) Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?
A) Amplitude of pendulum A is twice that of B.
B) Amplitude of B is twice of A.
C) Amplitude of A is 1.41 that of B.
D) Amplitude of B is 1.41 that of A.
E) Amplitude can not be determined from data given.
Answer: E
Diff: 1Var: 1Page Ref: Sec. 13.2
27) When the mass of a simple pendulum is tripled, the time required for one complete vibration
A) increases by a factor of 3.
B) does not change.
C) decreases to one-third of its original value.
D) decreases to 3/4 of its original value.
E) increases to 4/3 of its original value.
Answer: B
Diff: 1Var: 1Page Ref: Sec. 13.2
28) When the length of a simple pendulum is tripled, the time for one complete vibration increases by a factor of
A) 9.
B) 1/9.
C) 3.
D) 1/3.
E) .
Answer: E
Diff: 1Var: 1Page Ref: Sec. 13.2
FIGURE 13-3
29) Shown in Fig. 13-3 is a graph of position vs. time for a system undergoing simple harmonic motion. Which of the other graphs represents the system's velocity as a function of time?
A) graph a
B) graph b
C) graph c
D) graph d
Answer: B
Diff: 2Var: 1Page Ref: Sec. 13.2
30) A simple pendulum consists of a mass M attached to a weightless string of length L. For this system, when undergoing small oscillations
A) the frequency is independent of the length L.
B) the frequency is proportional to the amplitude.
C) the frequency is independent of the mass M.
D) the frequency is proportional to the period.
E) the period is proportional to the amplitude.
Answer: C
Diff: 2Var: 1Page Ref: Sec. 13.2